Ed8/3: Difference between revisions

Revision as of 23:42, 4 May 2025

The equal division of 8/3 (ed8/3) is a tuning obtained by dividing the Pythagorean perfect eleventh (8/3) in a certain number of equal steps.

Equivalence

Division of 8/3 into equal parts does not necessarily imply directly using this interval as an equivalence. Many, though not all, ed8/3 scales have a perceptually important false octave, with various degrees of accuracy.

The eleventh is the highest period where composers do not need to go beyond the false octave just to have a reasonably complete chordal harmony. The structural utility of 8/3 or another eleventh as a period may be undermined, though, by the fact that 8/3 is the avoid note in a major modality. This matters less in Mixolydian than it does in Ionian given that the former is the natural dominant scale anyway.

One approach to ed8/3 tunings is the use of the 3:4:5:6:(8) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone.

Joseph Ruhf's approach

This article or section contains multiple idiosyncratic terms. Such terms are used by only a few people and are not regularly used within the community.

Whereas in meantone it takes four 3/2 to get to 5/1, here it takes twelve octaves to get to 134217718/98415 (tempering out the schisma). So, doing this yields 7-, 10- and 17- or 13-, 16- or 19-note mos scales. While the notes are rather farther apart, the scheme is uncannily similar to the mohajira (within 8/3) temperaments. Joseph Ruhf calls this the Macromohajira Bolivarian mode.

Temperament areas

Galveston Bay Temperament Area

2L 8s and 8L 2s, 5L 5s - Galveston Symmetric, Pentachordal Major, Macro-Blackwood
4L 6s and 6L 4s - Baytown
3L 7s and 7L 3s - Bolivar

The similar decatonic scales in edIXs and edXs belong to the Chesapeake Bay Temperament Area:

Double Neapolitan[10i]: Scala Mariae/Notre Dame
Neapolitan/Middletown Valley Dorian[10i]: Annapolis
Middletown Valley Mixolydian[10i]: Oriole
Other similar decatonic ± 1 scales have the following names:
Locrian and Pluperfect/Abundant Phrygian[10i]/Lydian and Perfect Ionian[11i]: Scala Francisci
Perfect Ionian through Pluperfect/Abundant Phrygian[9i]: Montréal

Todo: review , cleanup, improve layout

@@ Line 8: / Line 8: @@
 One approach to ed8/3 tunings is the use of the 3:4:5:6:(8) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in [[meantone]].
-== Regular temperament approaches ==
+== Joseph Ruhf's approach ==
 {{idiosyncratic terms}}
 Whereas in meantone it takes four [[3/2]] to get to [[5/1]], here it takes twelve octaves to get to [[134217718/98415]] (tempering out the schisma). So, doing this yields 7-, 10- and 17- or 13-, 16- or 19-note [[mos scale]]s. While the notes are rather farther apart, the scheme is uncannily similar to the [[mohajira]] (within 8/3) temperaments. [[Joseph Ruhf]] calls this the ''Macromohajira Bolivarian mode''.